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Abstract In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $$n$$ items among which $$k$$ are defective, the smallest possible number of tests equals $$\min \{ C_{k,n} k \log n, n\}$$ up to lower-order asymptotic terms, where $$C_{k,n}$$ is a uniformly bounded constant (varying depending on the scaling of $$k$$ with respect to $$n$$) with a simple explicit expression. The algorithmic upper bound follows from a minor adaptation of an existing analysis of the Definite Defectives algorithm, and the algorithm-independent lower bound builds on existing works for the regimes $$k \le n^{1-\varOmega (1)}$$ and $$k = \varTheta (n)$$. In sufficiently sparse regimes (including $$k = o\big ( \frac{n}{\log n} \big )$$), our main result generalizes that of Coja-Oghlan et al. (2020) by avoiding the assumption $$k \le n^{1-\varOmega (1)}$$, whereas in sufficiently dense regimes (including $$k = \omega \big ( \frac{n}{\log n} \big )$$), our main result shows that individual testing is asymptotically optimal for any non-zero target success probability, thus strengthening an existing result of Aldridge (2019, IEEE Trans. Inf. Theory, 65, 2058–2061) in terms of both the error probability and the assumed scaling of $$k$$. 

The US highway system features a huge flux of energy transportation in terms of weight, speed, volume, flow density, and noise levels, with accompanying environmental effects. The adverse effects of high-volume traffic cause health concerns for nearby residential areas. Both chronic and acute exposure to PM 2.5 have detrimental effects on respiratory and cardiovascular health, and motor vehicles contribute 25–35% of direct PM 2.5 emissions. In addition to traffic-related pollutants, residing near major roadways is also associated with exposure to increased noise, and both affect the health and quality of life of residents. While regulatory and policy actions may reduce some exposures, engineering means may offer novel and significant methods to address these critical health and environmental issues. The goal of this study was to harvest highway-noise energy to induce surface charge via a piezoelectric material to entrap airborne particles, including PM 2.5. In this study, we experimentally investigated the piezoelectric effect of a polymethyl methacrylate (PMMA) sheet and ethylene propylene diene monomer (EPDM) rubber foam on the entrapment of copper (II)-2,4 pentanedione powder (Cu II powder). Appreciable voltages were induced on the surfaces of the PMMA via mechanical vibrations, leading to the effective entrapment of the Cu II powder. The EPDM rubber foam was found to attract a large amount of Cu II powder under simulated highway noise in a wide range, of 30–70 dB, and at frequencies of 700–1300 Hz, generated by using a loudspeaker. The amount of Cu II powder entrapped on the EPDM rubber-foam surfaces was found to scale with the SPL, but was independent of frequency. The experimental findings from this research provide a valuable base for the design of a robust piezoelectric system that is self-powered by harvesting the wasted sound energy from highway noise and reduces the amount of airborne particles over highways for effective environmental control.